Geostatistical analysis of rainfall variability on the plateau of Allada in South Benin

Naboua Kouhoundji et al. Int. Journal of Engineering Research and Applications www.ijera.com

ISSN: 2248-9622, Vol. 6, Issue 2, (Part - 4) February 2016, pp.42-48

www.ijera.com 42|P a g e

Geostatistical analysis of rainfall variability on the plateau of

Allada in South Benin

Naboua Kouhoundji*, Luc O. Sintondji**, Expédit W. Vissin***, Georges

A.Agbahungba* *(International Chair in Mathematical Physics and Applications (ICMPA- UNESCO Chair), University

ofAbomey-Calavi, Benin)

**(Laboratory of Hydraulics and Water Management, Department of Planning and Management of

Environment,University of Abomey-Calavi, Benin)

***(Pierre Pagney Laboratory Climate, Water, Ecosystem and Development, Department of Geography,

University of Abomey-Calavi, Benin)

ABSTRACT The goal of this survey is to contribute to a better understanding of the distribution of the rainfall on the plateau

of Allada in Benin. The plateau of Allada is the garner ofCotonou and vicinities. The food production is over

62% rainfed.Then, it imports to analyze the way how rains are spatially distributed on the area in order to deduct

the potential rainfall. To achieve this goal, rainfall data of 28 stations have been used. Three sub-periods have

been identified: 1996-2000, 2001-2005 and 2006-2010. The distribution of rainfall has been established with

Thiessen and kriging methods. On average, 1117mm of rain fell on the study area per year. But three tendencies

were shown: the less rainy zones, the fairly rainy zones, and the greatly rainy zones. All the rainfall zones knew

an increase of the precipitations except Abomey-Calavi and Niaouli. But the variations are not significant. While

analyzing the spatial structure for the kriging of precipitations, it was revealed a power model of variogram. The

direction of the rainfall gradient is oriented southeast - northwest during the three sub-periods. Abomey-Calavi

recorded the weakest precipitations. The strongest values are interchanged between Toffo and Sékou, Ouidah-

North and Ouidah-City.

Keywords-Rainfall gradient, South Benin, spatial structure, variogram.

I. INTRODUCTION The plateau of Allada, largest plateau of South

Benin, covers 2036 km2 (Fig.1). It hosts a population

of 717,813 inhabitants in 2013 with a density of 352

inhabitants per square kilometer (INSAE, 2015) [1].

It is located in the sub-equatorial area below the

parallel 6°60'where there is a unimodal rainfall

regime. It is an area whose agricultural sector is

characterized by its vulnerability to climate hazards

(Agbossou et al., 2012 [2]; Agossou et al., 2012 [3];

Allé et al., 2013 [4]). Climatic variations are a reality

and farmers are aware. These variations occur,

according to them, the lack of or insufficient rainfall,

its delays, bad distribution (Adjahossou et al., 2014

[5]). Meanwhile, this regionis known as food

products attic of the largest city of Benin (Cotonou)

and around. The food production is 62% rainfed

(Alléet al., 2013 [4]). Its increase is a key issue to

help ensure food and nutritional security of the

population (Sultan et al., 2012 [6]). The issue is

particularly important given that cereal imports have

not allowed to achieve food security and have led to

the impoverishment of populations (Goujon, 2010

[7];Ahomadikpohou, 2015 [8]). Understanding the

spatial distribution of the limiting factor (which is

rainfall) contributes to the realization of this issue.

Figure 1: Study area

RESEARCH ARTICLE OPEN ACCESS




This is to analyze, through a GIS tool

(geostatistics), the spatial discrimination of

precipitation from rainfall stations that cover the

study area.

II. DATA AND METHODS 2.1 DATA

The data used consist of ten rainfall stations

(obtained from the Agency for the Safety of Air

Navigation in Africa and Madagascar -Cotonou)

covering the study area. To better analyze the spatial

structure of rainfall, we took into account other

surrounding stations of southern and central Benin.

There are eighteen. Based on the work of Le Barbé et

al. (2002) [9], Balme et al. (2006) [10], Ali and Lebel

(2008) [11] and Sané et al. (2008) [12] on climate

disruptions in West Africa from the beginning of the

1970s, we chose the sub-period after 1990 (more

precisely 1995) for a recent analysis of changes.

Furthermore, in order to analyze the precipitation for

small step time, we have chosen five-year terms.

Thus, the sub-periods of precipitation are considered:

1996-2000 (P1), 2001-2005 (P2) and 2006-2010

(P3). This choice is justified by the fact that on the

same area, Allé et al. (2013) [13] studied the rain on

the steps of 20 years. Contrary to10 or 30 years step

time, five-year terms allow for a short-term picture of

rainfall variations. Agricultural production depends

on it.

2.2 METHODS

Thiessen method was used for the segmentation

of the study area into rainfall zones. Differences

between sub-periods of precipitation have been

evaluated by the parametric Student test. In the case

where the conditions of normality of data and

homogeneity of variances are not checked, the

alternative nonparametric Wilcoxon was used. All

this was done under the R3.1.3 software.

To better appreciate the distribution per point of

precipitation, the data have been geostatistically

analyzed (kriging method). Surfer 11.0 software was

used to carry out the distribution maps based on the

analysis of the appropriate variogram model. The

experimental variogram (Abramowitzand Stegun,

1972 [14]) was calculated by (1):

𝛾 𝑕 =1

2𝑁(𝑕) (𝑍𝑖 − 𝑍𝑗)2 𝑖 ,𝑗 ∈𝑆(𝑕) (1)

with:

𝛾 𝑕 ≡ 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑𝑣𝑎𝑟𝑖𝑜𝑔𝑟𝑎𝑚𝑓𝑜𝑟𝑎𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑕

𝑁 𝑕 ≡ 𝑛𝑢𝑚𝑏𝑒𝑟𝑜𝑓𝑐𝑢𝑝𝑙𝑒𝑠𝑜𝑓𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛𝑠

𝑠𝑒𝑝𝑎𝑟𝑎𝑡𝑒𝑑𝑏𝑦𝑎𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑕

𝑍𝑖𝑎𝑛𝑑𝑍𝑗 ≡ 𝑟𝑎𝑖𝑛𝑓𝑎𝑙𝑙𝑎𝑡𝑖𝑎𝑛𝑑𝑗𝑠𝑡𝑎𝑡𝑖𝑜𝑛𝑠

The variogram model used is evaluated by the

Nash criterion (Nash and Sutcliffe, 1970 [15]) whose

formula is (2):

𝑁𝑎𝑠𝑕 = 1 − (𝑌𝑖𝑜𝑏𝑠 −𝑌𝑖𝑚𝑜𝑑 )2𝑛1

(𝑌𝑖𝑜𝑏𝑠 −𝑌𝑚𝑜𝑦 )2𝑛1

(2)

with:

𝑌𝑖𝑜𝑏𝑠 ≡ 𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑒𝑑𝑟𝑎𝑖𝑛𝑓𝑎𝑙𝑙 𝑌𝑖𝑚𝑜𝑑 ≡ 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑𝑟𝑎𝑖𝑛𝑓𝑎𝑙𝑙 𝑌𝑚𝑜𝑦 ≡ 𝑚𝑒𝑎𝑛𝑜𝑓𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑒𝑑𝑟𝑎𝑖𝑛𝑓𝑎𝑙𝑙

The ordinary kriging method is used to estimate

precipitation values at unknown points. This is an

unbiased estimator widely used in hydrometry. This

method takes into account the influence (weight) of

the stations surrounding the unknown location. Any

precipitation value Z at a location x is estimated by

(3):

𝑍𝑥 = 𝜆𝑖 𝑍𝑖 (3)

Where𝑍𝑥 ≡ 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑𝑟𝑎𝑖𝑛𝑓𝑎𝑙𝑙 ;

𝑍𝑖 ≡ 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑𝑟𝑎𝑖𝑛𝑓𝑎𝑙𝑙 ; 𝜆𝑖 ≡ 𝑤𝑒𝑖𝑔𝑕𝑡𝑜𝑓𝑘𝑛𝑜𝑤𝑛𝑟𝑎𝑖𝑛𝑓𝑎𝑙𝑙

The 𝜆𝑖are calculated through the resolution of the

kriging system (4):

𝐾0𝜆𝑜 = 𝑘0𝜎𝑘02 = 𝜎𝑥

2 − 𝜆𝑜′ 𝑘0

𝜆𝑜 = 1𝑛𝑖=0

(4)

with

𝐾0 ≡ 𝑐𝑜𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒𝑚𝑎𝑡𝑟𝑖𝑥𝑜𝑓𝑎𝑙𝑙 𝑐𝑜𝑢𝑝𝑙𝑒𝑠𝑜𝑓𝑝𝑜𝑖𝑛𝑡𝑠

𝑘0 ≡ 𝑐𝑜𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒𝑚𝑎𝑡𝑟𝑖𝑥𝑜𝑓𝑎𝑙𝑙𝑐𝑜𝑢𝑝𝑙𝑒𝑠

𝑜𝑓𝑝𝑜𝑖𝑛𝑡𝑠𝑐𝑜𝑛𝑡𝑎𝑖𝑛𝑖𝑛𝑔𝑍𝑥

𝜎𝑘02 ≡ 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑖𝑜𝑛𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒𝑜𝑓𝑜𝑟𝑑𝑖𝑎𝑛𝑟𝑦𝑘𝑟𝑖𝑔𝑖𝑛𝑔

𝜎𝑥2 ≡ 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒𝑜𝑓𝑒𝑠𝑡𝑖𝑚𝑎𝑛𝑒𝑑𝑣𝑎𝑙𝑢𝑒𝑠

𝜆𝑜′ ≡ 𝑡𝑟𝑎𝑛𝑠𝑝𝑜𝑠𝑒𝑜𝑓𝑡𝑕𝑒𝑚𝑎𝑡𝑟𝑖𝑥𝜆𝑜

The first equation of the system (4) can be developed

like (5):

(5)

Surfer 11.0 software was used for thedifferent

calculations. Spatial analysis maps are performed

with the same software after ArcGIS 10.2 software

which was used to generate shape files (.shp).

Thiessen segmentation is performed using also

ArcGIS10.2.

III. RESULTS AND DISCUSSION The processing of data generated three types of

results: Evolutionof precipitations in the rainfall

zones, spatial structure of precipitations and spatio-

temporal distribution of rainfall.




Figure 2: Study area into rainfall zones

Figure 3: Mean and periodic rainfalls

3.1. EVOLUTION OF PRECIPITATIONS IN THE

RAINFALL ZONES

3.1.1. DELIMITATION OF RAINFALL ZONES AND

REGIONALIZATION OF PRECIPITATIONS

The segmentation method of Thiessen identified

10 rainfall stations that influence the study area

(Fig.2). These segments define homogeneous rainfall

zones. The areas covered by each of the zones vary

from 208 to 1018 km2 with an average of 658 (+/-

283) km2. These values show the surface disparity of

rainfall zones. The resulting spatial resolution is 51

km. This resolution is very loose in accordance with

the standards of the World Meteorological

Organization (WMO), which advocates 30-5 km

(WMO, 2012 [16]). This observation is identical to

that of Akponikpè and Lawin (2010) [17] intheir

work on the evaluation of observation systems and

research on climate change in Benin.

The 10 stations influencing the sector are part of

14 chosen by Allé et al. (2013) [4] in their study on

the evolution of intra-seasonal descriptors of rainy

seasons in South Benin between 1951 and 2010.

They chose these 14 stationsconsidering the

homogeneity of recorded rainfallvariances.

The average precipitation throughout the study

area during the study period (1996-2010) is 1117mm

per year. This value conceals disparities. Eastern

rainfall zones recorded the lowest rainfall values (less

than 1000mm / year) (Fig. 3). Those wereAdjohoun

and Abomey-Calavi. The majority of western zones

are moderately watered (1000 - 1200mm / year)

except Niaouli. That one was part of the wettest

zonesincludingOuidah-north and Ouidah-city

(rainfall more than 1200mm / year) (Fig. 3). This

presentation on trends in precipitation from 1996 to

2010 smooths sub-periods P1, P2 and P3.

3.1.2. CHANGES IN PRECIPITATIONS THROUGHOUT

SUB-PERIODS

Fifty percent (50%) of rainfall zones experienced

a decrease in total rainfall means between P1 and P2

(Fig. 4). Those wereBonou, Bopa, Niaouli, Ouidah-

city and Sekou. But the magnitudes of the declines

vary widely. While Bopa and Sekou decreased each

down to 11%, Bonou and Niaouli recorded

respectively 4% and 6% decrease (Fig. 5).That

decrease in rainfall amounts impacted negatively

food crops especially maize (Zea mays) and cowpea

(Vignaunguiculata). As examples, in the

Niaoulizone, maizedecreased in yield of 8% while in

Sékou, the decline was 15%. Cowpea, meanwhile,

had 9% and 17% decrease in yield respectively in the

twozones. The zones that experienced a perceptible

increase were 30%. Those were Abomey-Calavi,

Toffoand Ouidah-north. They have known

respectively 25, 14 and 8% increase (Fig. 5).

From P2 to P3, all the rainfall zones experienced

an increase in precipitation (though they were of




different magnitudes) except Abomey-calavi and

Toffo (Fig. 5). Those two zoneswere respectively

southeast and northwest of the study area. So, they

described the southeast - northwest axis (Fig. 3).

Overall throughout the study period (P1 to P3),

all the rainfall zones have experienced increased

precipitation with the exception of Abomey-calavi

and Niaouli (Fig. 5). Note that Niaouli is on the

southeast - northwest axis previously described by P2

to P3 rainfall (Fig. 3). It should be checked whether

the differences of precipitations fromP1 to P3 were

statistically significant.

According to the normality test of Shapiro-Wilk

at a confidence level of 95%, precipitations of P1 and

P3 are not normally distributed, while those of P2 are

(Table 1). Indeed, the probabilities obtained for P1

and P3 is less than 0.05 and that for P3 is greater than

0.05 (Table 1). It follows that the Wilcoxon test can

be used to assess the significance of the mean

differences of precipitations of sub-periods.

Figure 5: Precipitation variations between sub-

periods

Figure 4: Mean precipitations in rainfall zones

Table 1: Normality Test of Precipitations from P1 to

P3

Sub-

periods

Probability

(p-value) Decision

P1 0.022< 0.05

The precipitations of the

sub-period P1 are not

normally distributed

P2 0.824> 0.05


sub-period P2are


P3 0.032< 0.05


sub-period P3 are not


Applying the Wilcoxon test for P1-P2, P2-P3

and P1-P3, we obtained the results summarized in

Table 2.

Table 2: Significance test of mean differences of

precipitations from P1 to P3

Couples

ofperiod

s

Probability

(p-value) Decision

P1-P2 0.9118>0.05

There is no significant

difference between

precipitations of P1 and P2

P2-P3 0.1903>0.05


difference between


P1-P3 0.1903>0.05


difference between


25%

1%

1%

-4%

-11%

-6%

8%

-2%

-11%

14%

-22%

2%

6%

7%

16%

4%

2%

17%

22%

-6%

-2%

3%

6%

3%

3%

-2%

10%

14%

9%

7%

-40% -20% 0% 20% 40%

ABOMEY-CALAVI

ADJOHOUN

ALLADA

BONOU

BOPA

NIAOULI

OUIDAH-NORTH

OUIDAH-CITY

SEKOU

TOFFO

Rainfall (mm)

Rai

nfa

ll zo

nes

variP1P3 variP2P3 variP1P2

718

979

1098

1176

1131

1260

1163

1203

1166

1075

900

993

1106

1130

1008

1188

1256

1173

1041

1227

702

1013

1168

1206

1165

1241

1282

1368

1272

1149

0 300 600 900 1200 1500

ABOMEY-CALAVI

ADJOHOUN

ALLADA

BONOU

BOPA

NIAOULI

OUIDAH-NORTH

OUIDAH-CITY

SEKOU

TOFFO

Rainfall (mm)

Rai

nfa

ll zo

nes

P3 P2 P1




All the probabilities obtained are greater than

0.05 (Table 2). It is clear from this table, with a

confidence level of 95% that no difference exists

between the average rainfall of sub-periods P1, P2

and P3. However, from the agronomic point of view,

10mm of rain are very important for crops, especially

those who cannot tolerate a short period of dryness.

The examples given in thesection 3.1.2 about maize

and cowpea are illustratable. Therefore,it is necessary

to analyze the spatial structure of precipitation and

deduce the point distribution through the kriging

method.

3.2. SPATIAL STRUCTURE OF RAINFALL

The semi-variogram was the basis for the

analysis. Fig. 6 shows the evolution of the semi-

variograms of the observations versus distances

between rainfall stations and the simulation model

(Fig. 6).

Figure 6: Observed and simulated variograms

The variogram model is power-type (Fig. 6). It

admits no sill. The variance in the rainfall process on

the study area tends to infinity. So, there is a spatial

correlation among rainfalls recorded at the stations.

The Nash coefficient calculated (0.704) confirms this

status. Those rainfalls have regular trend in their

spatial distribution. They can therefore be modeled as

a function of X and Y coordinates of the stations. The

model admits a nugget effect. That reflects the

variations of the precipitations at small distances, so

small scale (within 20 km) (Fig. 6). The model

underestimates the variances between 20 and 50km

and after 170km, while it overestimates them

between 120 and 170km. The formula ofthe

variogram model ɣ is as follows:

𝛾 𝑕 = 18050 + 0.4779𝑕1.076 (6)

where h = distance between two points

This model is different from that obtained by

Lawin et al. (2010) [18] when they studied the

variability of rainfall scheme compared at regional

and local scales in the upper valley of Ouémé. They

had obtained an exponential model. They have used

daily rainfall throughout the period 1954-2005. That

model is also different from that obtained by Ly et al.

(2011) [19] when they studied daily

rainfallinterpolation at catchment scale by using

several variogram models in the Ourthe and Ambleve

catchments in Belgium. They found that the Gaussian

model was the most frequently observed.Allé et al.

(2013) [4], in their study of intra-seasonal descriptors

in south Benin, found also an exponential model.

This is related to the extent of their study area and a

larger number of stations they have taken into

account.

Spatial analysis allowed the productionof the

maps ofrainfall distribution of sub-periods in the

study area.

3.3. SPATIO-TEMPORAL DISTRIBUTION OF

RAINFALL

During the period P1 (1996-2000), the spatial

distribution of rainfall is shown on Fig. 7. Reading

that figure, we noted an overall rainfall gradient

southeast - northwest. The lowest rainfall is recorded

at Abomey-Calavi while the highest is recorded at

Niaouli. This observation is identical with the

Thiessen method of regionalization (Fig. 3 and

4).However, the method of Thiessen is more holistic.

Meanwhile it was assigning the yearly average of

720mm of rainfall for the entire zone of Abomey-

Calavi, the Kriging method said that this average

varies from 720 to 980mm per year. It is the same for

other rainfall zones where there is a spatial variation

of rainfall.

Figure 8: Precipitation distribution of P2





Figure 8 shows the spatial rainfall variations

throughout the sub-period P2 (2001-2005). Overall,

this sub-period was rainier than P1 (average annual

precipitation of 1102mm against 1096mm for P1).

The direction of the rainfall gradient was maintained

(southeast - northwest) with a particularity in Ouidah-

north. Abomey-Calavi was still recorded the lowest

rainfall from 900 to 1000mm per year. With the

Thiessen method, that zone was labeled900mm for

the same period (Fig. 3 and 4). About the

particularity of Ouidah-north and around, the average

annual rainfall oscillatedbetween 1260 and 1140mm.

That brings to observe that throughout that sub-

period, there were two poles of high rainfall: Toffoin

northwest and Ouidah-north insouthwest.


During the sub-period P3 (2006-2010), the same

direction of rainfall gradient was maintained. But

there had been a shift of the rainiest zone in the

northwest (Toffo) towardsSekou, in the same

direction. The wettest zone in southwest (Ouidah-

north) had moved westward (Ouidah-city). Overall,

this period is rainier than the two previous (1156mm

per year).

Those spatial distributions of rainfall are

expected to let have an idea aboutfive-year food

production of the study area. But it is not obvious.

The crops are sensitive to the beginning of wet

seasons, their intra-annual distribution and their

cessation (Allé et al., 2013 [13]).

IV. CONCLUSION This research is a contribution to the

understanding of the spatial and temporal distribution

of rainfall on the plateau of Allada. It is based on

precipitation data. Those data were averaged on five-

year time to better appreciate the changes. Two

methods were combined: the Thiessen method and

kriging method. The first method smooth the

spatialization of rainfall based on rainfall zones

influencing the study area. The second discriminates,

at 100m of spatial resolution, variations within

rainfall zones. On point of view coverage with

rainfall stations, spatial resolution is very loose

(51km instead of 30km). Precipitation

variationsalong sub-periods are not statistically

significant. But they can impact agricultural

production regardingthe sensitivity of cropsto water

factor. In this way, it is important to foresee the

impacts of these changes on the production of prime

crops on the study area. This will lead to initiate

sustainable management methods of the limiting

factor that is agricultural water.

V. ACKNOWLEDGEMENTS This work cannot be performed without

contributions of some institutions and persons. I

would like to thank the Network of Islamic

Associations and NGOs in Benin and the Association

of social solidarity in Benin (ASS) for their social

assistance. I thank also the promotion 2011 of Master

students at ICMPA. I have to remember the Chair

Holder Professor Hounkonnou M. Norbert and the

Scientific Secretary ProfessorBaloitchaEzinvi of

ICMPA for their scientific and administrative

support.

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